Will the stock returns be normally distributed? (minute-by-minute price increases from 2000 to 2026)?

The distribution of stock returns over such a long period (from 2000 to 2026) based on minute-by-minute price increases is usually not normal (Gaussian). Financial data often exhibit:

• "Heavy tails" — large deviations occur more frequently than in a normal distribution.
• Asymmetry — the distribution may be skewed to one side.
• Autocorrelation and volatility change over time (heteroskedasticity).

Therefore, for stock return analysis, distributions with heavy tails (e.g., Student's t-distribution) are often used, or methods that account for time dependence and volatility variability (e.g., GARCH models).

To test for normality, one can create a histogram of returns, a Q-Q plot, and conduct normality tests (e.g., Shapiro-Wilk test). However, in real financial market data, normality is almost always rejected.